A descriptor representation approach to observer-based H∞H∞ control synthesis for discrete-time fuzzy systems

This work is concerned with the observer-based H∞H∞ control synthesis problem of discrete-time Takagi–Sugeno (T–S) fuzzy systems with external disturbances. The objective is to find a new way to design the controller and observer guaranteeing a prescribed H∞H∞ performance of the fuzzy system. By the descriptor representation approach, two new conditions for observer-based H∞H∞ control synthesis are proposed based on various Lyapunov function candidates, which are in the form of linear matrix inequalities (LMIs). A numerical example will be given to show the efficiency of the proposed method.

► The present strict LMI method is a single step approach.
► The descriptor representation approach is developed for discrete-time T–S fuzzy systems.
► The paper might give the least conservative results for observer-based control.